Question: A palindrome is an integer that reads the same forward and backward, such as 3663. What percent of the palindromes between 100 and 500 contain at least one 5?
Since none of the palindromes between 100 and 500 begin with a 5, the only place a 5 can appear is in the tens digit.  Therefore, there are 4 palindromes between 100 and 500 with a 5: 151, 252, 353, and 454.  To count the total number of palindromes, we observe that there are 4 choices to make for the first/last digit and 10 choices to make for the middle digit.  Therefore, the percentage of palindromes that contain 5 as a digit is $\frac{4}{4\cdot 10}=\boxed{10\%}$.